Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#20259355 | C2 | semidirect |
| 3. C22×#15690277 | C2 | semidirect |
| 4. #27133239 | C2 | semidirect |
| 5. #27132828 | C2 | semidirect |
| 6. #27132820 | C2 | semidirect |
| 7. #27132657 | C2 | semidirect |
| 8. #27132631 | C2 | semidirect |
| 9. #419×C191 | C2 | semidirect |
| 140. C191 | #3011 | semidirect |
| 148. #419 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259370 | 2 |
| C2×#20259355 | 2 |
| C22×#15690277 | 2 |
| #27133239 | 2 |
| #27132828 | 2 |
| #27132820 | 2 |
| #27132657 | 2 |
| #27132631 | 2 |
| #419×C191 | 2 |
| #3011 | 191 |